A novel protocol for linearization of the Poisson-Boltzmann equation

TL;DR

This paper introduces a new protocol for linearizing the Poisson-Boltzmann equation, aligning it with the Debye-Huckel equation, and explores its implications for nano-bubbles in surfactant solutions.

Contribution

A novel linearization protocol for the Poisson-Boltzmann equation that simplifies electrostatic problem solving and reveals conditions for stable nano-bubbles.

Findings

Stable nano-bubbles can exist near the critical temperature with constant surface potential.

Nano-bubbles are unlikely to be stable with constant surface charge.

The protocol simplifies electrostatic calculations in complex systems.

Abstract

A new protocol for linearization of the Poisson-Boltzmann equation is proposed and the resultant electrostatic equation coincides formally with the Debye-Huckel equation, the solution of which is well known for many electrostatic problems. The protocol is examined on the example of electrostatically stabilized nano-bubbles and it is shown that stable nano-bubbles could be present in aqueous solutions of anionic surfactants near the critical temperature, if the surface potential is constant. At constant surface charge non nano-bubble could exist.